Machining tools such as drilling tools which have a tool head which serves to machine workpieces and a shank which supports the tool head are connected fixedly to a tool holder so as to rotate with it, which tool holder is in turn intended to be connected fixedly to a machine spindle so as to rotate with it, with the result that the machine can transmit a rotational movement of the tool. In particular, long machining tools or tool arrangements tend to vibrate during the machining operation. Here, the vibration of the tool arrangement which is assembled from the tool and the tool holder usually takes place in frequency ranges which are unpleasant for the human ear.